FINDING: Plimpton 322 encodes a primitive trigonometric table based on exact sexagesimal ratios, likely secants (or reciprocals of cosines) of angles in a regular right-triangle grid. MATH: - Each row corresponds to a normalized right triangle with short side \ (a \), long side \ (b \), and hypotenuse \ (c \) (all in sexagesimal integers). - The tablet lists \ ( (b², a, c) \) or equivalently \ ( (c² - a², a, c) \). - Key ratio: \ (= c / b \) (or \ (= c / a \) ), with angles decreasing from ~45° to ~30° in regular steps. - Sexagesimal base-60 system used: e. g. , row 1 gives \ (b = 1: 59 \) (119), \ (a = 2: 49 \) (169), \ (c = 2: 24 \) (144) → \ (c/b = 144/119 1. 2101 \), corresponding to \ (44. 76^ \). - No explicit equation for \ (\) or irrationals; all ratios are rational in base-60. CONNECTION: - The ratio sequence \ (c/b \) (secant) decreases from ~1. 4142 (√2) to ~1. 1547 (2/√3), spanning the golden ratio conjugate \ (Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Mon,) studied this question.